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Definability and Canonicity for Boolean Logic with a Binary Relation

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Języki publikacji
EN
Abstrakty
EN
This paper studies the concepts of definability and canonicity in Boolean logic with a binary relation. Firstly, it provides formulas defining first-order or second-order conditions on frames. Secondly, it proves that all formulas corresponding to compatible first-order conditions on frames are canonical.
Słowa kluczowe
Wydawca
Rocznik
Strony
301--327
Opis fizyczny
Bibliogr. 31 poz.
Twórcy
autor
  • Institut de recherche en informatique de Toulouse, CNRS — Universit´e de Toulouse 118 route de Narbonne, 31062 Toulouse Cedex 9, France
autor
  • Department of Mathematical Logic and Applications, Sofia University Blvd James Bouchier 5, 1126 Sofia, Bulgaria
Bibliografia
  • [1] Balbiani, P., Kikot, S.: Sahlqvist theorems for precontact logics. In: Advances in Modal Logic. Volume 9. College Publications (2012) 55–70.
  • [2] Balbiani, P., Tinchev, T.: Definability over the class of all partitions. Journal of Logic and Computation 16 (2006) 541–557.
  • [3] Balbiani, P., Tinchev, T.: Boolean logics with relations. Journal of Logic and Algebraic Programming 79 (2010) 707–721.
  • [4] Balbiani, P., Tinchev, T., Vakarelov, D.: Dynamic logics of the region-based theory of discrete spaces. Journal of Applied Non-Classical Logics 17 (2007) 39–61.
  • [5] Balbiani, P., Tinchev, T., Vakarelov, D.: Modal logics for region-based theories of space. Fundamenta Informaticæ 81 (2007) 29–82.
  • [6] Biacino, L., Gerla, G.: Connection structures: Grzegorczyk’s and Whitehead’s definition of point. Notre Dame Journal of Formal Logic 37 (1996) 431–439.
  • [7] Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press (2001).
  • [8] Chagrov, A., Chagrova, L.: The truth about algorithmic problems in correspondence theory. In: Advances in Modal Logic. Volume 6. College Publications (2006) 121–138.
  • [9] Chagrov, A., Zakharyaschev,M.: Modal Logic. Oxford University Press (1997).
  • [10] Clarke, B.: A calculus of individuals based on “connection”. Notre Dame Journal of Formal Logic 22 (1981) 204–219.
  • [11] Cohn, A., Hazarika, S.: Qualitative spatial representation and reasoning: an overview. Fundamenta Informaticæ 46 (2001) 1–29.
  • [12] Dimov, G., Vakarelov, D.: Contact algebras and region-based theory of space: a proximity approach – I. Fundamenta Informaticæ 74 (2006) 209–249.
  • [13] Dimov, G., Vakarelov, D.: Contact algebras and region-based theory of space: proximity approach – II. Fundamenta Informaticæ 74 (2006) 251–282.
  • [14] D¨untsch, I., Vakarelov, D.: Region-based theory of discrete spaces: a proximity approach. Annals of Mathematics and Artificial Intelligence 49 (2007) 5–14.
  • [15] Düntsch, I., Wang, H., McCloskey, S..: A relational algebraic approach to Region Connection Calculus. Theoretical Computer Science 255 (2001) 63–83.
  • [16] Düntsch, I., Winter, M.: A representation theorem for Boolean contact algebras. Theoretical Computer Science 347 (2005) 498–512.
  • [17] Galton, A.: The mereotopology of discrete space. In: Spatial Information Theory. Springer (1999) 251–266.
  • [18] Galton, A.: Qualitative Spatial Change. Oxford University Press (2000).
  • [19] Goldblatt, R., Thomason, S.: Axiomatic classes in propositional modal logic. In: Algebra and Logic. Springer (1975) 163–173.
  • [20] Grädel, E., Kolaitis, P., Vardi, M.: On the decision problem for two-variable first-order logic. Bulletin of Symbolic Logic 3 (1997) 53–69.
  • [21] Grzegorczyk, A.: Axiomatization of geometry without points. Synthese 12 (1960) 228–235.
  • [22] De Laguna, T.: Point, line and surface, as sets of solids. The Journal of Philosophy 19 (1922) 449–461.
  • [23] Mortimer, M.: On languages with two variables. Zeitschrift für mathematische Logik und Grundlagen der Mathematik 21 (1975) 135–140.
  • [24] Sahlqvist, H.: Completeness and correspondence in the first and second order semantics for modal logic. In: Proceedings of the Third Scandinavian Logic Symposium. North-Holland (1975) 110–143.
  • [25] Sambin, G., Vaccaro, V.: A new proof of Sahlqvist theorem on modal definability and completeness. The Journal of Symbolic Logic 54 (1989) 992–999.
  • [26] Stell, J.: Boolean connection algebras: a new approach to the region-connection calculus. Artificial Intelligence 122 (2000) 111–136.
  • [27] Vakarelov, D.: Region-based theory of space: algebras of regions, representation theory, and logics. In: Mathematical Problems from Applied Logic. Logics for the XXIst Century. II. Springer (2007) 267–348.
  • [28] Vakarelov, D., Dimov, G., Düntsch, I., Bennett, B.: A proximity approach to some region-based theory of space. Journal of Applied Non-Classical Logics 12 (2002) 527–559.
  • [29] De Vries, H.: Compact Spaces and Compactifications: an Algebraic Approach. Van Gorcum (1962).
  • [30] Wechler, W.: Universal Algebra for Computer Scientists. Springer (1992).
  • [31] Whitehead, A.: Process and Reality. MacMillan (1929).
Typ dokumentu
Bibliografia
Identyfikator YADDA
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